A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα 3
... remainder , until the remainder is equal to nothing ; the last divisor will be the greatest common divisor required . If any divisor contains a factor not contained in both the given quantities , that factor may be rejected . ( Bour ...
... remainder , until the remainder is equal to nothing ; the last divisor will be the greatest common divisor required . If any divisor contains a factor not contained in both the given quantities , that factor may be rejected . ( Bour ...
Σελίδα 36
... remainder will be ( a ) . ß $ If ( x ) x − ɑ , versely . - a is a root of p ( x ) = 0 ; and con- Every equation has at least one root . ( Du Bourguet , Ann . de Math . Tome 2. ) Every equation of n dimensions has n roots , and no more ...
... remainder will be ( a ) . ß $ If ( x ) x − ɑ , versely . - a is a root of p ( x ) = 0 ; and con- Every equation has at least one root . ( Du Bourguet , Ann . de Math . Tome 2. ) Every equation of n dimensions has n roots , and no more ...
Σελίδα 40
... remainder containing only y , which being made = 0 , will give the final equation required . If this equation be capable of solution , the values of a may be found by substituting those of y obtained from it , in the preceding remainder ...
... remainder containing only y , which being made = 0 , will give the final equation required . If this equation be capable of solution , the values of a may be found by substituting those of y obtained from it , in the preceding remainder ...
Σελίδα 53
... remainder contains only the first power of x , and may be represented by ƒ1 ( p , q ) x + ƒ2 ( p , q ) = 0 , then f ( p , q ) = 0 , and f2 ( p , q ) = 0 ; from which equations q may be eliminated , and the correspond- ing possible ...
... remainder contains only the first power of x , and may be represented by ƒ1 ( p , q ) x + ƒ2 ( p , q ) = 0 , then f ( p , q ) = 0 , and f2 ( p , q ) = 0 ; from which equations q may be eliminated , and the correspond- ing possible ...
Σελίδα 59
... 1p . -1 If a is such a number that no power of a < a2 - 1p , and a , a2 , a3 , ... a - 1 be respectively divided by p , the remainders will all be unequal . The values of a for all values of p from THE EQUATION y " ± p = 0 . 59 10.
... 1p . -1 If a is such a number that no power of a < a2 - 1p , and a , a2 , a3 , ... a - 1 be respectively divided by p , the remainders will all be unequal . The values of a for all values of p from THE EQUATION y " ± p = 0 . 59 10.
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Άλλες εκδόσεις - Προβολή όλων
A Synopsis of the Principal Formulae and Results of Pure Mathematics ... Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
A Synopsis of the Principal Formulae and Results of Pure Mathematics Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a-log a.sin a₁ a² a² angle arcs Assume ax² axis ay² B.cos B.sin b₁ Biot Bour c₁ centre circle co-ordinates conjugate diameters const continued fraction converging fraction cosec cosine curve cx² determined differential coefficients e₁ ellipse formula functions G. G. A. Ch given equation hyperbola integral intersection Let the equation log Cot log Sin log Sin Blog logarithmic m₁ method modulus negative obtained parabola perpendicular plane possible root prime number primitive equation quadratic divisor quadratic equation quotients R₁ radius reduced remainders sin x sine solution square straight line substituting subtangent Suppose surface tana tangent ternary divisor ternary form theorem triangle u₁ unknown quantities values vers x₁ y-y₁ y₁ απ
Δημοφιλή αποσπάσματα
Σελίδα 112 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Σελίδα 4 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Σελίδα 4 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 347 - Si, the formula assigned by Thomson to the mineral from Ireland, named " Anhydrous silicate of iron." Now, this slag had evidently been in a position favourable to the absorption of oxygen, namely, the...
Σελίδα 4 - To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common divisor.
Σελίδα 4 - The same quantity may be added to, or subtracted from, both sides of an equation. To...
Σελίδα 343 - The immutability, no less than the symmetry of its notation, (which should ever be guarded with a jealousy commensurate to its vital importance,) facilitates the translation of an expression into common language at any stage of an operation, - disburdens the memory of all the load of the previous steps, - and at the same time, affords it a considerable assistance in retaining the results.
Σελίδα 46 - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...
Σελίδα 161 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Σελίδα 2 - Tiie square root of a quantity cannot be partly rational and partly a quadratic surd. If possible, let...